ABSTRACT
This article presents an improved mathematical model and numerical simulation for weathering of large areas with complex topography. It uses the equations of momentum, temperature, and humidity in turbulent air and for heat and water infiltration into soils. A mathematical model is also presented to calculate the soil porosity fraction produced by physical rock weathering in areas where soil is produced from intrusive rocks (batholiths). An algorithm based on air velocity, humidity (rainfall), temperature variation, and soil topography was developed to quantify soil erosion and change of relief at each point and time step in air, at the ground surface, and within the soil. This results in a complete air-soil model based on conservation laws that have not previously been applied to large areas of the earth's surface. The mathematical model is solved using large-scale numerical simulations applied to an area of 6.6 km2 in the Sierra Nevada batholith of California, USA. The results show that the wind velocity and resulting erosion is greater in areas with steeper slopes and that moisture accumulates mainly in low and flat areas; therefore, erosion is not uniform throughout the study area. In addition, computer simulations localized calculations to discrete grid cells within the porous (saprolite) fraction of the soil produced by freezing and thawing of water in rock. Results indicate that this physical mechanism is the primary contributor to weathering of rock at the study area.
ABSTRACT
It is common in the numerical simulations for drying of food to suppose that the food does not experience a change of volume. The few numerical studies that include volume changes assume that the shrinkage occurs symmetrically in all directions. Therefore, this effect has not been fully studied, and it is known that not considering it can be detrimental for the accuracy of these simulations. The present study aims to develop a three-dimensional model for the simulation of fruits that includes the volume changes but also takes into consideration the asymmetry of the shrinkage. Physalis peruviana is taken as the subject of study to conduct experiments and imaging analyses that provided data about the drying kinetics and asymmetric shrinkage mode. The effective diffusion coefficient is found to be between 10-12 m2 s-1 and 1.75 × 10-9 m2 s-1. The shrinkage occurs essentially in only one direction, with an average velocity of 8.3 × 10-5 m/min. A numerical modelling scheme is developed that allows including the shrinkage effect in computer simulations. The performance of the model is evaluated by comparison with experimental data, showing that the proposed model decreases more than 4 times the relative error with respect to simulations that do not include volume changes. The proposed model proves to be a useful method that can contribute to more accurate modeling of drying processes.
ABSTRACT
A bi-dimensional diffusion mathematical model is proposed to study mass transfer in hollow fiber used for the concentration of juices by osmotic distillation (OD). The mathematical model was solved using the Finite Volume Method (FVM). The mass fraction at the boundaries was calculated by using the Functional-group Activity Coefficients (UNIFAC) method for the juice and by the Analytical Solutions Of Groups (ASOG) method for the brine. Calculated results were compared to an analytical solution for a case of mass diffusion in a cylinder with mass flow boundary condition. An algorithm to find the effective diffusion coefficient of gas through the membrane is proposed. To show its usefulness, different velocities were applied over the fiber surface to study the bi-dimensional effects that this velocity field has on the mass transfer inside the fiber. The results showed a maximum error of 5.6% when compared to experimental results.
